The clock is ticking quickly with the free-agent market set to open on Tuesday afternoon, but the Giants haven't given up hope of signing their starting tight end.

It appears they are making a late - and possibly last - push to re-sign Martellus Bennett before the free agent signing period begins. The two sides have talked in the last few days, according to a source, and plan to talk more before the deadline.

At the moment, though, there's no indication that an agreement is close.

"I am and will continue communicating with the Giants," Bennett's agent, Kennard McGuire, wrote in an email to the Daily News on Saturday. "Martellus is still in New York, and we are taking it one day at a time."

Re-signing the 26-year-old Bennett is one of the Giants' top goals this offseason, according to a team source. They were pleased with his play last season when he caught a career-high 55 passes for 626 yards and five touchdowns and proved to be a good blocker.

Eli Manning said Bennett was "more athletic than some of the tight ends we've had" with the Giants and there's a feeling in the organization that he has more potential to be tapped.